Transformations of quadratics

y=2(x-1)^2+1

y=-(x-3)^2-4

Given:

Length of a rectangular monitor screen is 5 in more than it's width.

If the length were doubled and if the width were deceased by 1 in the area would be increased by 170 in².

To find:

The length and width of the screen.

Solution:

Let width of the screen be x inches.

Length of a rectangular monitor screen is 5 in more than it's width. So,

Length of screen = (x+5) inches

Area of screen is

[tex]Area=length\times width[/tex]

[tex]A_1=(x+5)\times x[/tex]

[tex]A_1=x^2+5x\text{ in}^2[/tex]

If the length were doubled and if the width were deceased by 1 in the area would be increased by 170 in².

New length = 2(x+5) inches

New width = (x-1) inches

So, new area is

[tex]A_2=2(x+5)(x-1)[/tex]

[tex]A_2=(2x+10)(x-1)[/tex]

[tex]A_2=2x^2+10x-2x-10[/tex]

[tex]A_2=2x^2+8x-10 \text{ in}^2[/tex]

Area increased by  170 in².

[tex]A_2-A_1=170[/tex]

[tex](2x^2+8x-10)-(x^2+5x)=170[/tex]

[tex]2x^2+8x-10-x^2-5x=170[/tex]

[tex]x^2+3x-10=170[/tex]

Subtract 170 from both sides.

[tex]x^2+3x-10-170=0[/tex]

[tex]x^2+3x-180=0[/tex]

Splitting the middle term, we get

[tex]x^2+15x-12x-180=0[/tex]

[tex]x(x+15)-12(x+15)=0[/tex]

[tex](x+15)(x-12)=0[/tex]

[tex]x=-15,12[/tex]

Width cannot be negative. So, x=12.

Width = 12 inches

Length = 12+5 = 17 inches

Therefore, the length of screen is 17 inches and width is 12 inches.

Answer:

(8, 0 )

Step-by-step explanation:

Given the 2 equations

y = 8 - x → (1)

y = 5x - 40 → (2)

Substitute y = 5x - 40 into (1)

5x - 40 = 8 - x ( add x to both sides )

6x - 40 = 8 ( add 8 to both sides )

6x = 48 ( divide both sides by 6 )

x = 8

Substitute x = 8 into either of the 2 equations and solve for y

Substituting into (1)

y = 8 - 8 = 0

Solution is (8, 0 )

Answer:

D.

Step-by-step explanation:

I have been doing this in Geometry.

We know perpendicular means opposite recipicoles and opposite slopes.

so.. the slope is 3 to get the y-intercept you do this.

(1, 2) Use the points it gave you and the slope 3 and put it is y=mx + b form

2 = 3(1) + b (I do this because I don't know what b is yet) (b = y-intercept)

2 = 3 + b (subtract 3 on both sides)

-1 = b

The equation is y = 3x - 1

Answer:

MMMMMMMM

Step-by-step explanation:

Answer:

600 ≤ 3x ≤ 900

Can purchase between 200 to 300 tiles.

Step-by-step explanation:

600 ≤ 3x ≤ 900

600 ≤ 3x and 3x ≤ 900

x ≥ 200 and x ≤ 300

Answer:

No

Step-by-step explanation:

5/100 would be 0.05 as a decimal

Answer:

x ≥ 3

Step-by-step explanation:

The closed dot represents ≥ and ≤

The dot is located on the number "3"

The closed dot essentially shows that the solution is nothing more than 3 and up.

Let "x" be the variable we use.

x ≥ 3

Best of Luck!

The above never line shows the possible values of an variable in any expression.

Through Observation:

Hence, the required value of the variable can be equal to 3 or greater than 3 for that expression. This can be written as:

[tex] \large{ \boxed{ \rm{ x\geqslant 3}}}[/tex]

Carry On learning !

Answer:

x = - 4

Step-by-step explanation:

Given

[tex]\frac{5}{3}[/tex] x + 4 = [tex]\frac{2}{3}[/tex] x

Multiply through by 3 to clear the fractions

5x + 12 = 2x ( subtract 2x from both sides )

3x + 12 = 0 ( subtract 12 from both sides )

3x = - 12 ( divide both sides by 3 )

x = - 4

Given:

Able's age can be represented by x.

Able's sister is 4 years younger than him.

Able's older brother is twice as old as he is.

The combined age of all three siblings is 32.

To find:

The age of Able's younger sister.

Solution:

Able's age can be represented by x.

Able's sister is 4 years younger than him.

Age of Able's sister = (x-4)

Able's older brother is twice as old as he is.

Age of Able's older brother = 2x

The combined age of all three siblings is 32.

[tex]x+(x-4)+2x=32[/tex]

[tex]4x-4=32[/tex]

Add 4 on both sides.

[tex]4x=32+4[/tex]

[tex]4x=36[/tex]

Divide both sides by 4.

[tex]x=\dfrac{36}{4}[/tex]

[tex]x=9[/tex]

The age of Able is 9 years. So, age of his younger sister is

[tex]9-4=5[/tex]

Therefore, the age of Able's sister is 5 years.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Combined direction is

Combined velocity

Answer:

im gonna assume the 10 - 20 is what the equation is = to if not x wouldnt be = to anything x = -1.5

Step-by-step explanation:

-2.25x + 8.75x = 10-20

-2.25x+ 8.75x = -10

6.50x = -10 divide both sides by 6.5

x = -1.5

Answer:

1260

Step-by-step explanation:

Answer:

x = -8

Step-by-step explanation:

Hope This Helps!

Plz mark Brainliest

Answer:

x=−8

Step-by-step explanation:

Let's solve your equation step-by-step.

−6=3/8x−2+

1/8x

Step 1: Simplify both sides of the equation.

−6=3/8x−2+1/8x

−6=3/8x+−2+1/8x

−6=(3/8x+1/8x)+(−2)

(Combine Like Terms)

−6=1/2x+−2

−6=1/2x−2

Step 2: Flip the equation.

1/2x−2=−6

Step 3: Add 2 to both sides.

1/2x−2+2=−6+2

1/2x=−4

Step 4: Multiply both sides by 2.

2*(1/2x)=(2)*(−4)

Answer:

y = -1/3 x + 8/3 or 3y = -x + 8

Step-by-step explanation:

m = (-2 - 2) / [(6 - (-6)]

= -4 / 12

= -1/3

Use (-6, 2) and substitute in the formula:

y = mx + b

2 = -1/3 (2) + b

2 = -2/3 + b

2 + 2/3 = b

8/3 = b

y = mx + b

y = -1/3 x + 8/3 or 3y = -x + 8

Answer:

= 5/29

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)

    = ( 8-3)/(13 - -16)

    = ( 8-3)/( 13+16)

   = 5/29

He missed 2.

90% of 10 is 9. So he makes 9 shots and misses 1 for every 10 free throws.

So just double that number (1 shot missed) and so you get 2 missed shots

Hope this helps, and please consider marking branliest if this did

Step-by-step explanation:

1.2:3

2.2:5:5

3.5/4:3/2

4.5:4/3

Answer:

$840

Step-by-step explanation:

First, multiply 70 by $150 to get the total amount the Alonzo earned

70 x 150 = 10,500

Then, multiply 10,500 by 1.08 to find the total amount made with commissions.

10,500 x 11,340

Finally, subtract 10,500 from 11,340 to find the amount of money earned from commissions.

11,340 - 10,500 = 840

Answer:

$840

Step-by-step explanation:

Start by finding the total profit made:

70 • $150 = $10500

Then multiply the total by the commission rate, %8, which is equal to 0.08:

$10500 • 0.08 = $840

The answer is $840

Answer:

20

Step-by-step explanation:

4/4=1

4x5=20

20 1/4ths in 5 wholes

Answer:

20 fourths

Step-by-step explanation:

1 whole has 4 fourths.

5 wholes has 5 x 4 = 20 fourths.

Hope this helps.

Answer:

Triangle ABC is not a right triangle because d) it doesn't have a pair of perpendicular sides

Step-by-step explanation:

Perpendicular sides mean that the slopes are "opposite reciprocals" of each other.

Example: slope is 1/2 and the perpendicular line's slope is -2

How? 1/2 changes to 2 (you flip it, reciprocal), and then from 2 to -2 (apply opposite sign)

So when you calculate the slopes of AB, AC, and BC, none of their slopes are opposite reciprocals of each other. You can calculate the slopes of each and compare them if you want to check.

I really hope this helps, do you think you can tell me if you got the answer correct? I'd feel really bad if you got it wrong because of me. All I know is that it's not a right triangle.

Answer:

You can just mark the other person as brainliest.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

You can split it in many ways

for example, it can 164 + 2

160 + 4

100 + 66

and many more.........

hope this helps

plz mark as brainliest!!!!!!!!!!

Answer:

166/10=16.6

166/25=6.64

Step-by-step explanation:

true answer isssssss 7c-70

Step-by-step explanation:

50c -40c-70-3c

the answer is 7c - 70

Answer:

x = 14

Step-by-step explanation:

These angles are complementary angles, meaning they have a sum of 90°.

4x + 1 + 2x + 5 = 90

6x + 6 = 90 (Added like terms.)

6x = 84 (Subtracted 6 on both sides.)

x = 14 (Divided 6 on both sides.)

[tex]\sf \longmapsto \: (4x + 1) + (2x + 5)[/tex]

[tex]\sf \longmapsto \: 4x + 1 + 2x + 5 = 90[/tex]

[tex]\sf \longmapsto4x + 2x + 1 + 5 = 90[/tex]

[tex]\sf \longmapsto6x + 6 = 90[/tex]

[tex]\sf \longmapsto6x = 90 - 6[/tex]

[tex]\sf \longmapsto \: 6x = 84[/tex]

[tex]\sf \longmapsto \: x = \cancel\dfrac{84}{6} [/tex]

[tex]\sf \longmapsto \: x = 14[/tex]

[tex] \boxed{\sf \boxed {{ \sf \red{\: x = 14 }}}}[/tex]

Answer: It would be the last option, "Photograph." Graphic features found in the text are images, drawings, charts, graphs, etc.

Answer:

A

Step-by-step explanation:

It would be the first one.

Answer:

10.6

Step-by-step explanation:

To find the difference between 2 numbers, subtract the bigger one from the smaller one. In this case, 8.4-(-2.2) = 8.4 + 2.2 = 10.6

Answer: 2 - 2 + (2 + 2) × 0 = 0

Step-by-step explanation: there you go hope this helps also can I get brainliest